Finite Group Databasebeta

← #14763554

Subgroups — #14763554

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623150C211yesmaximal, characteristic
2C2×#10622333C211yesmaximal, characteristic, complemented
3#13071236C211yesmaximal, characteristic, complemented
4#13069583C211yesmaximal, characteristic, complemented
5#13069579C211yesmaximal, characteristic, complemented
6#13069438C211yesmaximal, characteristic, complemented
7#13069420C211yesmaximal, characteristic, complemented
8#13068938C211yesmaximal, characteristic, complemented
9#13068934C211yesmaximal, characteristic, complemented
10#13068931C211yesmaximal, characteristic, complemented
11#13068625C211yesmaximal, characteristic, complemented
12#13068624C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic, complemented
14#13068614C211yesmaximal, characteristic, complemented
15C11×#1875C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66993C2211yescharacteristic
19C2×#66992—21no—
20C2×#66991—21no—
21C2×D4×Dic11C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25#10623150—24no—
26#10623150C418yescomplemented
27C2×#66946C2211yescharacteristic
28C2×#66943C2211yescharacteristic
29C2×#66939—21no—
30C2×#66936—21no—
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622590C2211yescharacteristic
44#10622590C2211yescharacteristic
45#10622589C2211yescharacteristic
46#10622589C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49#10622559—21no—
50#10622559—21no—
51#10622541—21no—
52#10622541—21no—
53#10622333—24no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—21no—
66C22×C22⋊D11—21no—
67C22×C22⋊D11—21no—
68C23×Dic11—21no—
69C23×Dic11—21no—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#121—22no—
75C11×#121C2×C414yes—
76C11×#117—41no—
77C11×#117—41no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11D411yescharacteristic
86C2×C22⋊Dic11D411yescharacteristic
87#66993—22no—
88#66993C2×C414yescomplemented
89#66992—28no—
90#66991—28no—
91D4×Dic11—22no—
92D4×Dic11C2×C414yescomplemented
93#66983—22no—
94#66983C2×C414yes—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97#66979C2×C414yes—
98#66979D414yes—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—41no—
102C2×C4⋊Dic11—41no—
103C2×C4⋊Dic11D411yescharacteristic
104C2×C4⋊Dic11D411yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117#66946—22no—
118#66946C2×C414yescomplemented
119#66943—22no—
120#66943C2×C414yescomplemented
121#66939—28no—
122#66936—28no—
123C11×#102—41no—
124C11×#102—41no—
125C11×C22⋊C8—22no—
126#66896—41no—
127#66896—41no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C22⋊(C11⋊C8)—22no—
133#66885—41no—
134#66885—41no—
135#66879—22no—
136Dic11⋊C8—22no—
137Dic11⋊C8—22no—
138C8×Dic11—22no—
139#66873—41no—
140#66873—41no—
141#21872—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C23×D11—21no—
145C2×D4×C11—24no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—81no—
152C2×D4×C11—81no—
153C2×D4×C11C22×C412yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2411yescharacteristic
165C2×C22⋊D11—24no—
166C2×C22⋊D11—24no—
167C2×C22⋊D11—24no—
168C2×C22⋊D11—81no—
169C2×C22⋊D11—81no—
170C2×C22⋊D11—81no—
171C2×C22⋊D11—81no—
172C2×C22⋊D11—81no—
173C2×C22⋊D11—81no—
174C22×Dic11—24no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—42no—
179C22×Dic11—81no—
180C22×Dic11—81no—
181C22×Dic11—81no—
182C22×Dic11—81no—
183C22×Dic11C2×D411yescharacteristic
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44C22×C412yes—
193C2×C4×D11—24no—
194C2×C4×D11—81no—
195C2×C4×D11—81no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4C22×C412yes—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—42no—
210C42×C11—42no—
211C22⋊Dic11—24no—
212C22⋊Dic11C22⋊C414yes—
213C22⋊Dic11C22⋊C414yes—
214(C2×D11)⋊C4—24no—
215(C2×D11)⋊C4—24no—
216C4⋊Dic11—24no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—42no—
223C4⋊Dic11C22⋊C414yes—
224C4⋊Dic11C22⋊C414yes—
225C4⋊Dic11C22×C412yes—
226Dic11⋊C4—24no—
227Dic11⋊C4—81no—
228Dic11⋊C4—81no—
229Dic11⋊C4—81no—
230Dic11⋊C4—81no—
231C4×Dic11C22×C412yes—
232C4×Dic11C22×C412yes—
233C4×Dic11C2×D412yes—
234C4×Dic11C2×D412yes—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×#540—111no—
242C2×#433—111no—
243#2317—111no—
244#1992—111no—
245#1991—111no—
246#1961—111no—
247#1957—111no—
248#1875—111no—
249#1875D1111yescharacteristic, complemented
250#1874—111no—
251#1874—111no—
252#1804—111no—
253#1804—111no—
254#1802—111no—
255#1802—111no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—22no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11C2×C22⋊C412yes—
270C23×C11C22×D411yescharacteristic
271C22×D11—22no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278D4×C11—22no—
279D4×C11—22no—
280D4×C11—41no—
281D4×C11—41no—
282D4×C11—84no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11C2×C22⋊C412yes—
299C2×C4×C11C23×C411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11H(5,𝔽2)11yescharacteristic
302C2×C4×C11H(5,𝔽2)11yescharacteristic
303C2×C4×C112−1+411yescharacteristic
304C2×C4×C112−1+411yescharacteristic
305C22⋊D11—84no—
306C22⋊D11—84no—
307C22⋊D11—84no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—22no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—84no—
326C2×Dic11—84no—
327C2×Dic11C2×C22⋊C412yes—
328C2×Dic11C2×C22⋊C412yes—
329C2×Dic11C2×C22⋊C412yes—
330C2×Dic11C2×C22⋊C412yes—
331D44—22no—
332D44—22no—
333D44—41no—
334D44—41no—
335C4×D11—84no—
336C8×C11—41no—
337C8×C11—41no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340#540—118no—
341#540—224no—
342C2×#127—111no—
343C2×#125—111no—
344C2×#123—221no—
345C2×#123—221no—
346C2×#121—111no—
347C2×#121—221no—
348C2×#121—221no—
349C2×#121C2×D1111yescharacteristic
350C2×C4×D4—111no—
351C2×C4×D4—111no—
352C2×#117—111no—
353C2×#117C2×D1111yescharacteristic
354C22×C4⋊C4—111no—
355#433—224no—
356C2×C4⋊C8—111no—
357C2×C4⋊C8—111no—
358C2×#102—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102—111no—
363C2×#102—111no—
364C2×#102C2×D1111yescharacteristic
365C2×#102C2×D1111yescharacteristic
366C2×C22⋊C8—111no—
367C2×C22⋊C8C2×D1111yescharacteristic
368C2×#97—111no—
369C2×C4×C8—111no—
370#389—221no—
371#389—221no—
372#385—221no—
373#385—221no—
374#384—111no—
375#384—111no—
376#382—111no—
377#382—111no—
378#340—111no—
379#340—111no—
380#340—111no—
381#340—111no—
382#340—111no—
383#340—111no—
384#340C2×D1111yescharacteristic
385#340C2×D1111yescharacteristic
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11C22×C22⋊C411yescharacteristic
401C22×C11#53511yescharacteristic
402C22×C11#53611yescharacteristic
403C22×C11#57611yescharacteristic
404C22×C11#57611yescharacteristic
405C22×C11#57711yescharacteristic
406C22×C11#57711yescharacteristic
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—81no—
411C2×D11—81no—
412C2×D11—81no—
413C2×D11—81no—
414C4×C11—22no—
415C4×C11—42no—
416C4×C11—81no—
417C4×C11—81no—
418C4×C11#52011yescharacteristic
419C4×C11#52011yescharacteristic
420C4×C11#53711yescharacteristic
421C4×C11#53711yescharacteristic
422Dic11—22no—
423Dic11—22no—
424Dic11—22no—
425Dic11—22no—
426Dic11—42no—
427Dic11—81no—
428Dic11—81no—
429C22×D4—21no—
430C22×D4—111no—
431C22×D4—221no—
432C22×D4—221no—
433C22×D4—221no—
434C22×D4C22×D1111yescharacteristic
435C23×C4—221no—
436C23×C4—221no—
437C23×C4—221no—
438C23×C4C22×D1111yescharacteristic
439C22×C8—111no—
440C22×C8—111no—
441C22×C8C22×D1111yescharacteristic
442C22×C8C22×D1111yescharacteristic
443#127—114no—
444#127—222no—
445#125—114no—
446#125—222no—
447#123—228no—
448#123—228no—
449#121—22no—
450#121—114no—
451#121—228no—
452#121—228no—
453#121—222no—
454#121C4×D1114yes—
455C4×D4—114no—
456C4×D4—114no—
457C4×D4—222no—
458C4×D4—222no—
459#117—41no—
460#117—41no—
461#117—114no—
462#117—114no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—441no—
476C2×C4⋊C4—441no—
477C2×C4⋊C4C22×D1111yescharacteristic
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C4⋊C4C22×D1111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—111no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C42—21no—
488C2×C42—111no—
489C2×C42—111no—
490C4⋊C8—222no—
491C4⋊C8—222no—
492#102—41no—
493#102—41no—
494#102—441no—
495#102—441no—
496#102—441no—
497#102—441no—
498#102—441no—
499#102—441no—
500C22⋊C8—22no—
501C22⋊C8—222no—
502#97—222no—
503C4×C8—222no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508C2×C11—42no—
509C2×C11—82no—
510C2×C11#231111yescharacteristic
511C2×C11#289711yescharacteristic
512C2×C11#289711yescharacteristic
513C2×C11#322011yescharacteristic
514C2×C11#322111yescharacteristic
515C2×C11#324111yescharacteristic
516C2×C11#324111yescharacteristic
517D11—82no—
518C24—21no—
519C24—221no—
520C24D4×D1111yescharacteristic
521C2×D4—24no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—81no—
528C2×D4—81no—
529C2×D4—112no—
530C2×D4—224no—
531C2×D4—224no—
532C2×D4—224no—
533C2×D4—221no—
534C2×D4—221no—
535C2×D4—221no—
536C2×D4—221no—
537C2×D4—221no—
538C2×D4—881no—
539C2×D4—881no—
540C2×D4—881no—
541C2×D4—881no—
542C2×D4—881no—
543C2×D4—881no—
544C2×D4C2×C4×D1112yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—111no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—224no—
557C22×C4—224no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—442no—
562C22×C4—881no—
563C22×C4—881no—
564C22×C4—881no—
565C22×C4—881no—
566C22×C4—881no—
567C22×C4—881no—
568C22×C4C2×C4×D1112yes—
569C22×C4D4×D1111yescharacteristic
570C22×C4D4×D1112yes—
571C22×C4C23×D1111yescharacteristic
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—114no—
590C4⋊C4—114no—
591C4⋊C4—112no—
592C4⋊C4—224no—
593C4⋊C4—224no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—442no—
600C4⋊C4—881no—
601C4⋊C4—881no—
602C4⋊C4—881no—
603C4⋊C4—881no—
604C4⋊C4C2×C4×D1112yes—
605C22⋊C4—24no—
606C22⋊C4—42no—
607C22⋊C4—114no—
608C22⋊C4—114no—
609C22⋊C4—224no—
610C22⋊C4—224no—
611C22⋊C4—224no—
612C42—42no—
613C42—112no—
614C42—112no—
615C42—112no—
616C42—112no—
617C11#2187211yescharacteristic, complemented, Sylow
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—222no—
632C23—441no—
633C23—441no—
634C23—441no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23C22⋊C4×D1112yes—
639C23C2×D4×D1111yescharacteristic
640D4—22no—
641D4—22no—
642D4—41no—
643D4—41no—
644D4—84no—
645D4—222no—
646D4—222no—
647D4—441no—
648D4—441no—
649D4—884no—
650D4—884no—
651D4—884no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—112no—
668C2×C4—112no—
669C2×C4—112no—
670C2×C4—112no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—222no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—884no—
689C2×C4—884no—
690C2×C4—884no—
691C2×C4C22⋊C4×D1112yes—
692C2×C4C22×C4×D1111yescharacteristic
693C2×C4C2×D4×D1111yescharacteristic
694C2×C4#6703711yescharacteristic
695C2×C4#6703711yescharacteristic
696C2×C4#6704311yescharacteristic
697C2×C4#6704311yescharacteristic
698C8—41no—
699C8—41no—
700C8—441no—
701C8—441no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—442no—
717C22—442no—
718C22—442no—
719C22—881no—
720C22—881no—
721C22—881no—
722C22—881no—
723C22C2×C22⋊C4×D1111yescharacteristic
724C22#1062312311yescharacteristic
725C22#1062317911yescharacteristic
726C22#1062330011yescharacteristic
727C22#1062330111yescharacteristic
728C22#1062330511yescharacteristic
729C22#1062330611yescharacteristic
730C4—22no—
731C4—42no—
732C4—81no—
733C4—81no—
734C4—222no—
735C4—222no—
736C4—222no—
737C4—222no—
738C4—442no—
739C4—881no—
740C4—881no—
741C4#1062307711yescharacteristic
742C4#1062307711yescharacteristic
743C4#1062312811yescharacteristic
744C4#1062312811yescharacteristic
745C2—42no—
746C2—82no—
747C2—882no—
748C2#1307120311yescharacteristic
749C2#1307713811yescharacteristic
750C2#1307714111yescharacteristic
751C2#1307966411yescharacteristic
752C2#1307967511yescharacteristic
753C2#1307986711yescharacteristic
754C2#1307987511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1875C2
socleC23×C11C22×D4
prime radicalC2×#10623150C2
cosocleC22×C4×C11C24
hypercenter#1875D11
hypocenterC11#21872
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10622333C2semidirect
3. #13071236C2semidirect
4. #13069583C2semidirect
5. #13069579C2semidirect
6. #13069438C2semidirect
7. #13069420C2semidirect
8. #13068938C2semidirect
9. #13068934C2semidirect
10. #13068931C2semidirect
11. #13068625C2semidirect
12. #13068624C2semidirect
13. #13068615C2semidirect
14. #13068614C2semidirect
15. C11×#1875C2semidirect
26. #10623150C4semidirect
88. #66993C2×C4semidirect
92. D4×Dic11C2×C4semidirect
118. #66946C2×C4semidirect
120. #66943C2×C4semidirect
249. #1875D11semidirect
617. C11#21872semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106231502
C2×#106223332
#130712362
#130695832
#130695792
#130694382
#130694202
#130689382
#130689342
#130689312
#130686252
#130686242
#130686152
#130686142
C11×#18752
#2187211